Question for Moderators of Homework Section

[hotvette]

Would it be against the philosophy of this forum to post a brief tutorial on a given topic, in this specific case, elementary motion (e.g. free falling object, trajectories, straight line motion, block on an incline w/ and w/o friction)?

The emphasis of the tutorial would be on methodology (i.e. develoment and use of free body diagram to derive the basic equation of motion based on the FDB). The methodology is exactly the same for each of the above problems mentioned above.

In the brief time I've been participating in this great forum (i.e. lots of participation), I've noticed time and time again the same things:

- don't have a clue how to even begin
- I have an equation but I'm not sure how to use it or if it applies
- etc.

My thought is that a basic tutorial on the fundamentals might just by chance get at least some of the students going in the right direction on their own (of course, they'd need to read and try to understand it).

Anyway, it was just an idea I had. I'd be willing to write it if the moderators would be willing to comment, edit, reject altogether, etc. If this is a bad idea, just say so. I won't be offended. Just trying to help where I perceive a need.

 

[Integral]

Absolutely not against any policy. Such things have been discussed but have not happened. Post your presentation, we can then all review it. If it comes up to muster, it will be stickied.

This is a great, thank you for the offer, I am looking forward to seeing it. I have noticed and appreciated your posts.

 

[ZapperZ]

I don't think it is a bad idea at all. I've been guilty of promising to write such a thing, but never followed through.

You are more than welcome to write it (I'm being presumptious for speaking on behalf of the HW section moderators). However, don't be discouraged if a lot of these people don't read it. A lot of them have managed to ignore the Sticky's in various parts of the forum instructing them on where to post their homework questions and how to post their homework questions.

Zz.

 

[hotvette]

Thanks for your comments and encouragement. Gosh, I'm on the hook, now! I'll see what I can come up with. It may take a little time between work, kids, etc.

I realize that many may not read it, but I wouldn't hesitate to reply to a post by saying 'read this (link) first and try it before you ask for help'

Doodling for the Tutorial:

The change in velocity (acceleration) with which an object moves
is directly proportional to the magnitude of the force applied to the
object and inversely proportional to the mass of the object.

Mathematically, this can be stated: $$\vec F = m \vec a$$
where F and a are vector quantities.

$$\Sigma F_x = m a_x \ \ or \ \ \Sigma F_x = m \ \frac {dv_x}{dt} \ \ or \ \ \Sigma F_x = m \ \frac{d^2x}{dt^2} \ \ or \ \ \Sigma F_x = m \ \ddot x$$

$$\Sigma F_y = m a_y \ \ or \ \ \Sigma F_y = m \ \frac {dv_y}{dt} \ \ or \ \ \Sigma F_y = m \ \frac{d^2y}{dt^2} \ \ or \ \ \Sigma F_y = m \ \ddot y$$

$$m \ g = m \ \frac{dv_y}{dt}$$
Separating the variables, dividing both sides by m, and
integrating we get:

$$\int g dt = \int dv_y \ \ \Longleftrightarrow \ \ gt \ + \ C_1 = v_y \ + \ C_2 \ \ \Longleftrightarrow \ \ v_y = gt \ + \ C_1 \ - \ C_2$$

$$v_y = g \ t + C_1 - C_2 \Longleftrightarrow g \ t + v_{y0}$$

$$dx/dt = v_x \Longleftrightarrow \int dx = \int v_x \ dt$$

$$v_y = g \ t \ + \ v_{y0} = dy/dt \ \ \Longleftrightarrow \ \ \int dy = \int (gt \ + \ v_{y0}) dt$$

$$y = \frac{1}{2} g t^2 \ + \ v_{y0}t \ + \ y_0$$

$$\Sigma F_y = m a_y: \ \ mg = ma_y \ \ or \ \ g = a_y$$

$$\Theta$$

$$\mu N$$

$$\Sigma F_x = m a_x: \ \ mg \sin(\theta) = ma_x \ \ or \ \ g \sin(\theta) = a_x$$

$$\frac{dv_x}{dt} = g \sin(\theta) \ \ \Longleftrightarrow \ \ v_x = g \sin(\theta) t + v_{x0}$$

 

[ZapperZ]

Thanks for your comments and encouragement. Gosh, I'm on the hook, now! I'll see what I can come up with. It may take a little time between work, kids, etc.

I realize that many may not read it, but I wouldn't hesitate to reply to a post by saying 'read this (link) first and try it before you ask for help'

I'm copying this onto my hard drive, and after the 12 million'th time and you are now shouting "READ THE DAMN LINK, WHY DON'T YOU??!", I'll post this to you as a reminder!

:) :)

Zz.

 

[Moonbear]

Thanks for your comments and encouragement. Gosh, I'm on the hook, now! I'll see what I can come up with. It may take a little time between work, kids, etc.

I think that's what happened to the good intentions of all the others who have suggested the same thing. Seriously, if you're up for it, go for it!

I'm copying this onto my hard drive, and after the 12 million'th time and you are now shouting "READ THE DAMN LINK, WHY DON'T YOU??!", I'll post this to you as a reminder!

 

[hotvette]

Draft #1 for Moderator review and comment.

Actually, I just had a thought. Maybe 1 page on the Newton's 2nd law and the integraton thereof - a little more formal than what I have here. Then, 1 pagers after that looking at specific applications.

 

[quantumdude]

Hotvette, that is really nice! Thanks for doing it.

I've played with the idea of doing something like this, but never did it because of two very discouraging reasons. One, most students who post HW questions here do so because they either don't read their book or can't understand it, which would imply that the same students either won't read or can't understand any summary that I could write. And the second reason is that posted announcements are almost universally ignored by students posting HW questions. Just look at how many students post HW questions without making any attempt to solve the problem on their own, despite my notices that say, "Read this before posting."

Well, I don't mean to be too much of a downer, and this is certainly worth a try. The only thing about your attachment that I would comment on right now is that there is a blank "page 3" that can probably be cropped off, unless it is reserved for future additional material.

 

[Pyrrhus]

Yes, the problem with most students in the homework section is that they don't understand the hints or whatnots, because they don't read their book. On the worst case, they have homework, and they want someone to do it for them. I've also notice some students are taken General Physics I, and they don't even know what is a vector! . It could be either their fault or the college's.

Someone might want to write a tutorial on vector algebra

 

[honestrosewater]

(Can we see it too? )

 

[Moonbear]

(Can we see it too? )

Oh goody, my first chance to use my superpowers! (I didn't even realize it wasn't approved until I saw your note, I'm not used to this yet, heh heh. )

Nice job hotvette. I'm impressed by how quickly you jumped on the idea and ran with it! Fantastic!

 

[hotvette]

Draft # 2 for Moderator Review. Work in process - two more pages to come (incline plane, projectile)

 

[Ivan Seeking]

Very nice!

 

[saltydog]

Good for you Hotvette. The proof in the pudding is to obtain feed-back from students, others who tell you they had problems understanding this concept until they read your explanation.

 

[hotvette]

I tried to post draft #3 but it seems there is a 100k limit on file size. I have 6 pages that total 151k in a pdf. Splitting apart won't work - page 5 by itself is 110k in size! What to do?

Gee, I just noticed the homework helper symbol. I'm honored! Is this because of the # of posts I've had or did y'all bestow this upon me?

After some fooling around I managed to get it split into 2 files that are each < 100k. They need some cleaning up, but it's basically done. Appreciate any and all editorial comments. Also, can someone verify that the math is correct?

Fyi, my objective was to have no topic span more than one page to minimize loss of interest.

P.S. I was going to edit an earlier post of mine in this same thread to delete the doodles (equations), but I can't seem to edit it.

 

[Integral]

Very nice,
They open and are readable but I get an error when I open them. I am not sure if I can see all of them.
I would like to get this posted so we can get some feedback from the students.

 

[Moonbear]

No problem opening them here. Very nicely done hotvette!

And you were awarded the medal by the PF staff for your efforts in homework help. Congrats and thanks!

 

[Dr Transport]

I'd like to see the files also, they would not open on my box...same error as Integral

 

[hotvette]

Thanks everyone for your comments. You need Acrobat 6.0 to open them. It's free, so shouldn't be a problem to get it. That's how I was able to get the size down (by restricting it to 6.0 only).

Don't spend too much time on what I've posted. I just cleaned up the examples to make them absolutely identical in format. All I have to do is tweak the Epilog page and I'll post what I consider the final version. Just give me 30-60 minutes. Later.

 

[hotvette]

OK everyone, attached is what I consider the final version, unless anyone can suggest additions to the Epilog page (at the end).

P.S. Many thanks to the PF staff for the Homework Helper medal!

 

[Pyrrhus]

I like the presentation of the work, i haven't read it yet, i'll do so when i get time, I'm pretty busy these days.

 

[ZapperZ]

Do we post our comments here? If we are, then here's mine. :)

I've had time to look at the first one, but not the 2nd, so this is all I have for now. Most of these comments are "trivial", but for completeness sake and for clarity, I think they should be considered.

1. "The change in velocity (acceleration)... " should be, to be accurate, the time rate of change in velocity. It's a difference between $$\Delta(v)$$ and $$dv/dt$$.

2. In the example of using Newton's 2nd Law under the influence of gravity, we need to be a bit more explicit in explaining how we are able to write

$$mg = m \frac{dv_y}{dt}$$

This equation implicitly assumes that we have already established a coordinate system in which the direction of mg is in the positive direction. There is nothing to prevent someone from writing mg with a minus sign if that person defined the positive direction in the opposite way. It is only after the coordinate system is established can one write the differential equation of motion.

I think this is crucial because in many cases, students are stuck at the very beginning and don't know where to start or how to start. While to most of us, being able to write that equation is almost second nature, it really isn't to most students learning this. I still see many who don't quite understand why they should do it this way.

3. The same comment goes for the free fall example. While a diagram is there, I think it makes sense to be explicit in describing our thinking of how we came up with the differential equation. This is required right in the very beginning, not at the end after it is solved, because this is needed to be able to write the equation properly in the first place.

Zz.

 

[Astronuc]

I believe this matter has been discussed in one form or another, e.g. in this thread -

Physics HW FAQ Discussion - https://www.physicsforums.com/showthread.php?t=71931

Perhaps this could be done in a type of Wikibook or like the Physics Blog that Greg put together. I think perhaps the editing should be restricted to Science Advisors, Homework helpers, as well as Super Mentors.

The issue then becomes - how to get new members to check such resources before posting a question. It appears sometimes that people do not read "Read this before posting" nor the "FAQ's" sections.

BTW - hotvette's work looks really good. Nice pdfs!

 

[saltydog]

Got a good one for you Hotvette:

Check out "No Idea where to start" in the HW. Tell me what you see happens. Up to you.

 

[Moonbear]

1. "The change in velocity (acceleration)... " should be, to be accurate, the time rate of change in velocity. It's a difference between $$\Delta(v)$$ and $$dv/dt$$.

Zz, I see your point and understand the reason to change it, however, is there any other way to word it that would be correct? It took me a moment to process the wording there, so I can just imagine a struggling student just glazing over and getting completely stuck at that point. Something, perhaps, like the change in velocity over time or the change in velocity as time passes. I know it's important to convey it's not just that the velocity changes, but how that velocity is changing over a period of time.

I think this is important because it's one of those real fundamentals that the slightest difficulty with it sets the student up for recurring difficulty throughout, but if this concept "clicks" for them, then they are ready to grasp further material. I just remember being taught that stuff the first time with graphs and had no idea how the area under a curve of a graph had anything at all to do with anything in the real world. I understood that a car accelerates, but we weren't taught it that way, so the concepts quickly became mathematical abstractions rather than concrete understanding (i.e., we learned to plug numbers into equations rather than learn to understand why those equations represented something in the physical world).

 

[robphy]

Nice work, Hotvette.

I hope it's not too late to suggest a few pedagogical changes in your methodology.

1. Draw the FBD. [This does not need a coordinate system to be introduced.]
2. Write down Newton's Second Law, vectorially. [e.g., $$(\vec N+\vec W)=m\vec a$$ for the incline problem]

I claim that a lot of the "physics" is already done at this stage. Indeed, if the above steps are done incorrectly, mathematics won't save you.

3. Now, introduce your coordinate systems and write the component form of Newton's law. [This is mainly math. Here, you see the angles and the signs come into the calculation. In step 2, before the coordinate system, one is literally writing down "the vector sum of the forces on the object"... and not worrying about pluses and minuses and cosines and sines.] At this stage, I tell my students: one can use ANY coordinate system to finish the problem... some choices will lead to an easier mathematics problem than others.

In addition, it may be advantageous to substitute (expressions in parentheses) for vector components. For example, $$W_y = m a_y$$ becomes $$(-mg) = m a_y$$. First, it suggests that all you did was substitute. In addition, it suggests that the minus sign arises from the choice of coordinates.

4... etc...


Otherwise, it looks fine.
I look forward to more tutorials. Great effort!

 

[hotvette]

This is good - thanks for all of your comments. This is what I was looking for. It will take a while to crawl through and decipher them.

I do ask a favor though - pls direct your comments to the specific page. I can't always tell from reading the comments which page is being referred to.

Re the Newton's 2nd Law page, I don't have any vested interest in how it's worded, so any suggested changes are fine with me. I'm neither physicist nor scientist, so whatever y'all think is fine. My only very strong desire is to have it be confined to a single page.

Re the individual problems, I am willing to make minor changes, such as being more explicit about the choice of coordinate system sooner rather than later, but I really like the structure and flow and don't want to change things too much. Again, single page only.

I could really use some help on the last page (Epilog). My intention is for it to serve as a wrap up.

Lastly, I don't want this review/comment/revision process to last very long. Everyone (myself particularly) will lose interest and it all will be for naught. Plus, we all have other things to do.

Oh, I forgot. Re someone's comment about 'future tutorials', my only comment is: $$ha!$$

P.S.

Getting the 'right' answer is important, but understanding how to solve the problem (i.e. how you get the right answer) is just as important, if not more so.

I love it. Mind if I use a variation of this on the 1st page?

 

[hotvette]

Got a good one for you Hotvette:

Check out "No Idea where to start" in the HW. Tell me what you see happens. Up to you.

Sorry, I don't follow. Pls explain.

 

[Astronuc]

Getting the 'right' answer is important, but understanding how to solve the problem (i.e. how you get the right answer) is just as important, if not more so.

I love it. Mind if I use a variation of this on the 1st page?

Be my guest. I think any of us who have taught share a similar philosophy. I don't just want the right answers, I want my students to really understand the math and the physics.

In the real world, there are no answers in the back of the book!

And in the real world of engineering, the wrong answer can be very expensive to correct, or worse - can cause fatalities.

 

[cscott]

I believe this matter has been discussed in one form or another, e.g. in this thread -

Physics HW FAQ Discussion - https://www.physicsforums.com/showthread.php?t=71931

Perhaps this could be done in a type of Wikibook or like the Physics Blog that Greg put together. I think perhaps the editing should be restricted to Science Advisors, Homework helpers, as well as Super Mentors.

You stole my idea! ...kidding

 

[loseyourname]

Zz, I see your point and understand the reason to change it, however, is there any other way to word it that would be correct? It took me a moment to process the wording there, so I can just imagine a struggling student just glazing over and getting completely stuck at that point. Something, perhaps, like the change in velocity over time or the change in velocity as time passes. I know it's important to convey it's not just that the velocity changes, but how that velocity is changing over a period of time.

Personally, I think the best way to verbally state this is "the change in velocity with respect to the change in time," and this statement should be accompanied by an explanation stating that velocity can also change with respect to other variables. The point seems to get across best through the use of graphs, where the student can clearly see the two axes on which different variable are mapped. Visually apprehending the relationship can help a great deal.

 

[hotvette]

Ok gang, I've incorporated as best I can the comments that have been made. Pls don't be offended if is isn't exactly what you intended.

My personal opinion is that we're at the point of greatly diminishing returns unless there is something glaring that is unclear or confusing. My overriding objective is no more than 1 page per topic. Anyway, have a read of what I believe to be the final, final version.

 

[amcavoy]

I had a brilliant idea last night at 3am (why do all brilliant ideas seem to come at 3am when your mind is racing from injesting far too much caffine during the day?) to include a couple of examples using different choices of coordinate systems. So, I did the free falling body and block on incline problems again w/ different coordinate systems. This will hopefully show the impact of choosing an appropriate coordinate system.

Anyway, here goes, and this one is it, done, finished, final, fertig, fini, finito, terminado, befejezett, обработанный, 出来上がる

Those look really good. This is definitely going to help in the homework section!

Alex

 

[hotvette]

Thanks. So, unless the Moderators and/or PF staff have an objection, I guess the next step is to place this as a sticky in the Homework Section? Is there anything I need to do or will someone else do it?

Sure would appreciate it if someone were to check the math, first, though. I believe it is correct, but it is always good to have fresh eyes look at it.

 

[Gokul43201]

I've added hotvette's files into the HW discussion thread in Gen Physics. This also contains Marlon's and arildno's tutorials.

https://www.physicsforums.com/showthread.php?p=780118#post780118

Hotvette, that's a real spiffy tute. Thanks !

I too have written up a tutorial on tackling force problems - aimed at high school (pre-calc) students. I've just got to put in a couple more figures and it will be done. Hope to add it to the existing list of tutorials soon.